If molality of the dilute solution is doubled, the value of molal depression constant $\left({\mathrm{K}}_{\mathrm{f}}\right)$ will be

$K_f=\frac{R{T}_{f^0}^2}{1000{\mathrm{\Delta }}_{f}H}$
The molar, depression constant (kf) is a characteristic property of the solvent. Hence, it is not affected by molality. It depends on (i) Nature of solvent (ii) Molal enthalpy of fusion.